AAEC 6524: Environmental Theory and Policy Analysis

Transcription

1 AAEC 6524: Environmental Theory and Policy Analysis Environmental Policies under imperfect information Part C Klaus Moeltner Spring 2017 February 6, / 27

2 Outline 2 / 27

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5 Outline 2 / 27

6 So far: Uncertainty about firms cost structure taken as given. Choose policy instruments to minimize (unavoidable) welfare losses, given uncertainty. Alternative: Design abatement contracts that make it in the firm s best interest to reveal its true MAC. The development of such a contractual framework is called Design (MD) 3 / 27

7 So far: Uncertainty about firms cost structure taken as given. Choose policy instruments to minimize (unavoidable) welfare losses, given uncertainty. Alternative: Design abatement contracts that make it in the firm s best interest to reveal its true MAC. The development of such a contractual framework is called Design (MD) 3 / 27

8 So far: Uncertainty about firms cost structure taken as given. Choose policy instruments to minimize (unavoidable) welfare losses, given uncertainty. Alternative: Design abatement contracts that make it in the firm s best interest to reveal its true MAC. The development of such a contractual framework is called Design (MD) 3 / 27

9 So far: Uncertainty about firms cost structure taken as given. Choose policy instruments to minimize (unavoidable) welfare losses, given uncertainty. Alternative: Design abatement contracts that make it in the firm s best interest to reveal its true MAC. The development of such a contractual framework is called Design (MD) 3 / 27

10 Design Origins in principal-agent s There, asymmetric and incomplete information amongst players (= workers, firms, agencies) with different incentives produce sub-optimal outcomes. Objective: Design mechanisms (= contracts, regulatory interventions) that align the incentives of all players. A successful MD will make self-interested actions lead to preferred group outcomes. 4 / 27

11 Design Origins in principal-agent s There, asymmetric and incomplete information amongst players (= workers, firms, agencies) with different incentives produce sub-optimal outcomes. Objective: Design mechanisms (= contracts, regulatory interventions) that align the incentives of all players. A successful MD will make self-interested actions lead to preferred group outcomes. 4 / 27

12 Design Origins in principal-agent s There, asymmetric and incomplete information amongst players (= workers, firms, agencies) with different incentives produce sub-optimal outcomes. Objective: Design mechanisms (= contracts, regulatory interventions) that align the incentives of all players. A successful MD will make self-interested actions lead to preferred group outcomes. 4 / 27

13 Design Origins in principal-agent s There, asymmetric and incomplete information amongst players (= workers, firms, agencies) with different incentives produce sub-optimal outcomes. Objective: Design mechanisms (= contracts, regulatory interventions) that align the incentives of all players. A successful MD will make self-interested actions lead to preferred group outcomes. 4 / 27

14 Firms Incentives Quantities: Firms have incentives to over-state costs. Prices (taxes): Firms have incentices to under-state costs. Emissions will (far) exceed societal optimum. 5 / 27

15 Firms Incentives Quantities: Firms have incentives to over-state costs. Prices (taxes): Firms have incentices to under-state costs. Emissions will (far) exceed societal optimum. 5 / 27

16 Firms Incentives Quantities: Firms have incentives to over-state costs. Prices (taxes): Firms have incentices to under-state costs. Emissions will (far) exceed societal optimum. 5 / 27

17 Firms Incentives Quantities: Firms have incentives to over-state costs. Prices (taxes): Firms have incentices to under-state costs. Emissions will (far) exceed societal optimum. 5 / 27

18 Contract features Incentive-compatible: Firm s best strategy is to reveal true cost structure. Individually rational: Firm finds it in its best interest to participate. 6 / 27

19 Contract features Incentive-compatible: Firm s best strategy is to reveal true cost structure. Individually rational: Firm finds it in its best interest to participate. 6 / 27

20 Kwerel (1976) Hybrid policy of permits L and subsidy ζ for unused permits Firms report abatement costs C j (e j). Regulator constructs AMAC C (E) Chooses L, ζ accordingly, i.e. s.t. D (L) = C (L) = ζ. 7 / 27

21 Kwerel (1976) Hybrid policy of permits L and subsidy ζ for unused permits Firms report abatement costs C j (e j). Regulator constructs AMAC C (E) Chooses L, ζ accordingly, i.e. s.t. D (L) = C (L) = ζ. 7 / 27

22 Kwerel (1976) Hybrid policy of permits L and subsidy ζ for unused permits Firms report abatement costs C j (e j). Regulator constructs AMAC C (E) Chooses L, ζ accordingly, i.e. s.t. D (L) = C (L) = ζ. 7 / 27

23 Kwerel (1976) Hybrid policy of permits L and subsidy ζ for unused permits Firms report abatement costs C j (e j). Regulator constructs AMAC C (E) Chooses L, ζ accordingly, i.e. s.t. D (L) = C (L) = ζ. 7 / 27

24 Kwerel s claim Under this policy structure: 1. Firms will truthfully reveal their marginal abatement cost, and 2. Regulator can choose L = E, ζ = ζ to achieve the socially obtimal outcome. 8 / 27

25 Kwerel s claim Under this policy structure: 1. Firms will truthfully reveal their marginal abatement cost, and 2. Regulator can choose L = E, ζ = ζ to achieve the socially obtimal outcome. 8 / 27

26 Kwerel s claim Under this policy structure: 1. Firms will truthfully reveal their marginal abatement cost, and 2. Regulator can choose L = E, ζ = ζ to achieve the socially obtimal outcome. 8 / 27

27 Firm s problem: mintc j = C j (e j ) + σē j ζ (ē j e j ) (1) e j,ē j 9 / 27

28 Scenario 1 If σ > ζ, no incentives to hold unused permits, and e j = ē j, j, and C j (e j) = σ, j In the aggregate, this implies C (L) = σ 10 / 27

29 Scenario 1 If σ > ζ, no incentives to hold unused permits, and e j = ē j, j, and C j (e j) = σ, j In the aggregate, this implies C (L) = σ 10 / 27

30 Scenario 1 If σ > ζ, no incentives to hold unused permits, and e j = ē j, j, and C j (e j) = σ, j In the aggregate, this implies C (L) = σ 10 / 27

31 Scenario 2 σ < ζ is infeasible in equilibrium Arbitrage will drive prices up to σ = ζ 11 / 27

32 Scenario 2 σ < ζ is infeasible in equilibrium Arbitrage will drive prices up to σ = ζ 11 / 27

33 Scenario 3 If σ = ζ, we get C j (e j) = ζ, j In the aggregate, this implies C (L) = ζ 12 / 27

34 Scenario 3 If σ = ζ, we get C j (e j) = ζ, j In the aggregate, this implies C (L) = ζ 12 / 27

35 Scenario 3 If σ = ζ, we get C j (e j) = ζ, j In the aggregate, this implies C (L) = ζ 12 / 27

36 Equilibrium price Therefore, we must have σ = max {ζ, C (L)} Since, by definition, D (L) = ζ, this further implies σ = max {D (L), C (L)} (2) 13 / 27

37 Equilibrium price Therefore, we must have σ = max {ζ, C (L)} Since, by definition, D (L) = ζ, this further implies σ = max {D (L), C (L)} (2) 13 / 27

38 Equilibrium price Therefore, we must have σ = max {ζ, C (L)} Since, by definition, D (L) = ζ, this further implies σ = max {D (L), C (L)} (2) 13 / 27

39 Equilibrium price Therefore, we must have σ = max {ζ, C (L)} Since, by definition, D (L) = ζ, this further implies σ = max {D (L), C (L)} (2) 13 / 27

40 Key insight Consider efficient outcome E, s.t., as always, D (E ) = C (E ) KEY: (2) implies that σ (L) > σ (E ) for any L E So reporting C (E) = C (E) is in the best interest of the firms 14 / 27

41 Key insight Consider efficient outcome E, s.t., as always, D (E ) = C (E ) KEY: (2) implies that σ (L) > σ (E ) for any L E So reporting C (E) = C (E) is in the best interest of the firms 14 / 27

42 Key insight Consider efficient outcome E, s.t., as always, D (E ) = C (E ) KEY: (2) implies that σ (L) > σ (E ) for any L E So reporting C (E) = C (E) is in the best interest of the firms 14 / 27

43 Generalized version of Holds even if permit market is not perfectly competitive Regulator auctions off fixed number of permits based on firms reported costs NEW: Then reimburses firms a fraction of the revenue 15 / 27

44 Generalized version of Holds even if permit market is not perfectly competitive Regulator auctions off fixed number of permits based on firms reported costs NEW: Then reimburses firms a fraction of the revenue 15 / 27

45 Generalized version of Holds even if permit market is not perfectly competitive Regulator auctions off fixed number of permits based on firms reported costs NEW: Then reimburses firms a fraction of the revenue 15 / 27

46 Generalized version of Holds even if permit market is not perfectly competitive Regulator auctions off fixed number of permits based on firms reported costs NEW: Then reimburses firms a fraction of the revenue 15 / 27

47 Highlights Efficient: In equilibrium, get truthful report and socially optimal emission Equitable: Firms end up paying amount proportional to their individual emissions General: Holds for a wide variety of market settings Relatively easy to implement 16 / 27

48 Highlights Efficient: In equilibrium, get truthful report and socially optimal emission Equitable: Firms end up paying amount proportional to their individual emissions General: Holds for a wide variety of market settings Relatively easy to implement 16 / 27

49 Highlights Efficient: In equilibrium, get truthful report and socially optimal emission Equitable: Firms end up paying amount proportional to their individual emissions General: Holds for a wide variety of market settings Relatively easy to implement 16 / 27

50 Highlights Efficient: In equilibrium, get truthful report and socially optimal emission Equitable: Firms end up paying amount proportional to their individual emissions General: Holds for a wide variety of market settings Relatively easy to implement 16 / 27

51 Single-firm case 1. Firm submits marginal abatement cost schedule C (E) 2. Regulator sells L permits at price σ, s.t. C (L) = D (L) = σ 3. Firms pays σl, receives L permits 4. Regulator returns amount β (L) σl to firm 17 / 27

52 Single-firm case 1. Firm submits marginal abatement cost schedule C (E) 2. Regulator sells L permits at price σ, s.t. C (L) = D (L) = σ 3. Firms pays σl, receives L permits 4. Regulator returns amount β (L) σl to firm 17 / 27

53 Single-firm case 1. Firm submits marginal abatement cost schedule C (E) 2. Regulator sells L permits at price σ, s.t. C (L) = D (L) = σ 3. Firms pays σl, receives L permits 4. Regulator returns amount β (L) σl to firm 17 / 27

54 Single-firm case 1. Firm submits marginal abatement cost schedule C (E) 2. Regulator sells L permits at price σ, s.t. C (L) = D (L) = σ 3. Firms pays σl, receives L permits 4. Regulator returns amount β (L) σl to firm 17 / 27

55 Firm s problem Firm must decide on which cost function to submit. She knows that the regulator will react to it with a L, σ combo. So in essence, firm gets to choose L and σ Using D (L) = σ, we can reduce this to a one-parameter problem, the choice of L. 18 / 27

56 Firm s problem Firm must decide on which cost function to submit. She knows that the regulator will react to it with a L, σ combo. So in essence, firm gets to choose L and σ Using D (L) = σ, we can reduce this to a one-parameter problem, the choice of L. 18 / 27

57 Firm s problem Firm must decide on which cost function to submit. She knows that the regulator will react to it with a L, σ combo. So in essence, firm gets to choose L and σ Using D (L) = σ, we can reduce this to a one-parameter problem, the choice of L. 18 / 27

58 Firm s problem Firm must decide on which cost function to submit. She knows that the regulator will react to it with a L, σ combo. So in essence, firm gets to choose L and σ Using D (L) = σ, we can reduce this to a one-parameter problem, the choice of L. 18 / 27

59 Firm s problem, cont d min L TC (L) = C (L) + D (L) L β (L) D (L) L (3) 19 / 27

60 FOC C (L) + D (L) + D (L) L β (L) D (L) L β (L) (D (L) + D (L) L) = 0 (4) 20 / 27

61 Regulator s problem For social optimum, we need C (L) + D (L) = 0 Setting second line in (4) to zero and solving for β (L) yields: β (L) = 1 D (L) D (L) L (5) 21 / 27

62 Regulator s problem For social optimum, we need C (L) + D (L) = 0 Setting second line in (4) to zero and solving for β (L) yields: β (L) = 1 D (L) D (L) L (5) 21 / 27

63 Regulator s problem Plugging (5) into (3) yields min L TC (L) = C (L) + D (L) (6) This naturally leads to the social optimum 22 / 27

64 Regulator s problem Plugging (5) into (3) yields min L TC (L) = C (L) + D (L) (6) This naturally leads to the social optimum 22 / 27

65 Regulator s problem Plugging (5) into (3) yields min L TC (L) = C (L) + D (L) (6) This naturally leads to the social optimum 22 / 27

66 Closer look at β β (L) = 1 D(L) D (L)L By curvature properties of D (L), we have β {0, 1} If D (L) = αl, optimal β = 0 (emission tax set at constant marg. damage level) In general, regulator will set 0 < β < / 27

67 Closer look at β β (L) = 1 D(L) D (L)L By curvature properties of D (L), we have β {0, 1} If D (L) = αl, optimal β = 0 (emission tax set at constant marg. damage level) In general, regulator will set 0 < β < / 27

68 Closer look at β β (L) = 1 D(L) D (L)L By curvature properties of D (L), we have β {0, 1} If D (L) = αl, optimal β = 0 (emission tax set at constant marg. damage level) In general, regulator will set 0 < β < / 27

69 Closer look at β β (L) = 1 D(L) D (L)L By curvature properties of D (L), we have β {0, 1} If D (L) = αl, optimal β = 0 (emission tax set at constant marg. damage level) In general, regulator will set 0 < β < / 27

70 Extreme case: β = 1 (when it shouldn t) Figure 4.8: Montero with =0 or =1 Incentive for firm to over-state costs $ C ( E) D ( E) $ C ( E) * * j k i h g f c 0 L * b L a Ê C ( E) ˆ E E 0 l L e L * d Panel A Panel B 24 / 27

71 Extreme case: β = 1 (when it shouldn t) Figure 4.8: Montero with =0 or =1 Incentive for firm to over-state costs $ C ( E) D ( E) $ C ( E) * * j k i h g f c 0 L * b L a Ê C ( E) ˆ E E 0 l L e L * d Panel A Panel B 24 / 27

72 Extreme case: β = 0 (when it shouldn t) 39 0 or =1 Incentive for firm to under-state costs D ( E) $ C ( E) D ( E) * j k i h g f c C ( E) ˆ E E 0 l L e L * d ˆ E C ( E) E Ê Panel B 25 / 27

73 Extreme case: β = 0 (when it shouldn t) 39 0 or =1 Incentive for firm to under-state costs D ( E) $ C ( E) D ( E) * j k i h g f c C ( E) ˆ E E 0 l L e L * d ˆ E C ( E) E Ê Panel B 25 / 27

74 Montero mechanism for multiple firms Figure 4.9: Montero for firm j $ C ( E) C ( e ) j j D ( e ) j j D ( E) b a C ( E ) j j 0 e j ê j E -j E E e j 26 / 27

75 Uncertainty over costs makes efficiency properties differ across policy instruments Weizman: Instrument choice boils down to relative magnitude of (absolute values of) slopes of D (E) and C (E) Ex-post inefficiency remains Can be made arbitrarily small using hybrid instruments (Spence & Roberts 1976, Unold & Requate 2001) Alternative to minimizing ex-post loss : Design Can achieve ex-post efficiency 27 / 27

76 Uncertainty over costs makes efficiency properties differ across policy instruments Weizman: Instrument choice boils down to relative magnitude of (absolute values of) slopes of D (E) and C (E) Ex-post inefficiency remains Can be made arbitrarily small using hybrid instruments (Spence & Roberts 1976, Unold & Requate 2001) Alternative to minimizing ex-post loss : Design Can achieve ex-post efficiency 27 / 27

77 Uncertainty over costs makes efficiency properties differ across policy instruments Weizman: Instrument choice boils down to relative magnitude of (absolute values of) slopes of D (E) and C (E) Ex-post inefficiency remains Can be made arbitrarily small using hybrid instruments (Spence & Roberts 1976, Unold & Requate 2001) Alternative to minimizing ex-post loss : Design Can achieve ex-post efficiency 27 / 27

78 Uncertainty over costs makes efficiency properties differ across policy instruments Weizman: Instrument choice boils down to relative magnitude of (absolute values of) slopes of D (E) and C (E) Ex-post inefficiency remains Can be made arbitrarily small using hybrid instruments (Spence & Roberts 1976, Unold & Requate 2001) Alternative to minimizing ex-post loss : Design Can achieve ex-post efficiency 27 / 27

79 Uncertainty over costs makes efficiency properties differ across policy instruments Weizman: Instrument choice boils down to relative magnitude of (absolute values of) slopes of D (E) and C (E) Ex-post inefficiency remains Can be made arbitrarily small using hybrid instruments (Spence & Roberts 1976, Unold & Requate 2001) Alternative to minimizing ex-post loss : Design Can achieve ex-post efficiency 27 / 27

80 Uncertainty over costs makes efficiency properties differ across policy instruments Weizman: Instrument choice boils down to relative magnitude of (absolute values of) slopes of D (E) and C (E) Ex-post inefficiency remains Can be made arbitrarily small using hybrid instruments (Spence & Roberts 1976, Unold & Requate 2001) Alternative to minimizing ex-post loss : Design Can achieve ex-post efficiency 27 / 27